How do I fit a 3rd order polynomial Basis using fitrgp?

Hello,

I am trying to fit a 3rd order polynomial basis using fitgrp for my signal (1x1503). From the instructions, it looks like I would pass hfcn but don't quite understand how to implement this for the 3rd order polynomial. How would I do this?

Here is code but at the moment it is only implementing a quadratic:

t_observed = (0:length(dodWavelet(:,1))-1)/10;
y_observed = dodWavelet(:,1);

gprMdl1 = fitrgp(t_observed',y_observed,'Basis',"pureQuadratic");

[ypred1] = predict(gprMdl1,t_observed');

Answer 1

[Star Strider]

From the documentation, using a table as input:

• Each row of Tbl corresponds to one observation, and each column corresponds to one variable.

So the data must be column-oriented.

Taking a clue from the 'pureQuadratic' function, see if this does what you want —

dodWavelet = randn(1,1503).' + sin(2*pi*(0:1502).'/500);                           % Create Data (Note Transposition To Column Vector)
t_observed = (0:length(dodWavelet(:,1))-1)/10;
y_observed = dodWavelet(:,1);
hfcn = @(X) [ones(size(X)) X X.^2 X.^3];
B0 = rand;
gprMdl1 = fitrgp(t_observed',y_observed,'Basis',hfcn, 'Beta',B0);

format long
Coefficients = gprMdl1.Beta

Coefficients = 4x1

-0.050399516294833 0.004117034993237 -0.000011969492060 -0.000000227385782

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format short

[ypred1,ysd1, yint1] = predict(gprMdl1,t_observed');

figure
hp1 =  plot(t_observed, y_observed, '.', 'DisplayName','Data');
hold on
hp2 = plot(t_observed, ypred1, '-r', 'DisplayName','Regression');
hp3 = plot(t_observed, yint1, '--r', 'DisplayName','95% Confidence Limits');
hold off
grid
legend([hp1 hp2 hp3(1)], 'Location','best')

It seems to work and produce a reasonable result.

EDIT — (30 May 2024 at 22:03)

Added ‘Coefficients’ assignment to display them.

.

[FsC]

thank you!

[Star Strider]

As always, my pleasure!